Dynamic-factor models

Stata’s dfactor estimates the parameters of
dynamic-factor models by maximum likelihood. Dynamic-factor models are
flexible models for multivariate time series in which the observed
endogenous variables are linear functions of exogenous covariates and
unobserved factors, which have a vector autoregressive structure. The
unobserved factors may also be a function of exogenous covariates. The
disturbances in the equations for the dependent variables may be
autocorrelated.

We have data on industrial production (ipman), real disposable income
(income), weekly hours worked (hours), and the unemployment rate
(unemp). We suspect there exists a latent factor that can explain
all four of these series, and we conjecture that latent factor follows an
AR(2) process.

Even more interesting is the path of our unobserved factor. We have
hypothesized that all our observed variables follow the unobserved latent
factor. We can obtain the one-step predictions of the factor by typing

. predict factor, factor

We can then trace the path of the factor by graphing the result:

. tsline factor

Extracting the latent factor in this manner is sometimes referred to as
extracting or estimating an indicator.

dfactor also estimates the parameters of static-factor models,
seemingly unrelated regression (SUR) models, and vector autoregressive (VAR)
models by maximum likelihood. dfactor allows for constraints on the
covariance matrix of the errors in an SUR model and a VAR model.

After estimation, you can predict both the endogenous variables and the
unobserved factors. In addition to one-step predictions, dfactor can
produce dynamic multistep predictions.